Question

a rectangle is removed from a right triangle to create the shaded region shown below. find the area of the shaded region. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate area of the right - triangle

The formula for the area of a right - triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. Here, the base of the right - triangle is $4 + 3=7$ yd and the height is $2+3 = 5$ yd. So, $A_{triangle}=\frac{1}{2}\times7\times5=\frac{35}{2}=17.5$ yd².

Step2: Calculate area of the rectangle

The formula for the area of a rectangle is $A_{rectangle}=length\times width$. Here, the length of the rectangle is 3 yd and the width is 2 yd. So, $A_{rectangle}=3\times2 = 6$ yd².

Step3: Calculate area of the shaded region

The area of the shaded region $A$ is the area of the right - triangle minus the area of the rectangle. So, $A=A_{triangle}-A_{rectangle}=17.5 - 6=11.5$ yd².

Answer:

$11.5$ yd²